Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks
The batch split-complex backpropagation (BSCBP) algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/329173 |
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| _version_ | 1832563877035900928 |
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| author | Huisheng Zhang Chao Zhang Wei Wu |
| author_facet | Huisheng Zhang Chao Zhang Wei Wu |
| author_sort | Huisheng Zhang |
| collection | DOAJ |
| description | The batch split-complex backpropagation (BSCBP) algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to zero. By adding a moderate condition, the weights sequence itself is also proved to be convergent. A numerical example is given to support the theoretical analysis. |
| format | Article |
| id | doaj-art-e61ae57dded743dda74e0ca4eb98eb0f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e61ae57dded743dda74e0ca4eb98eb0f2025-02-03T01:12:19ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/329173329173Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural NetworksHuisheng Zhang0Chao Zhang1Wei Wu2Applied Mathematics Department, Dalian University of Technology, Dalian 116024, ChinaApplied Mathematics Department, Dalian University of Technology, Dalian 116024, ChinaApplied Mathematics Department, Dalian University of Technology, Dalian 116024, ChinaThe batch split-complex backpropagation (BSCBP) algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to zero. By adding a moderate condition, the weights sequence itself is also proved to be convergent. A numerical example is given to support the theoretical analysis.http://dx.doi.org/10.1155/2009/329173 |
| spellingShingle | Huisheng Zhang Chao Zhang Wei Wu Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks Discrete Dynamics in Nature and Society |
| title | Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks |
| title_full | Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks |
| title_fullStr | Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks |
| title_full_unstemmed | Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks |
| title_short | Convergence of Batch Split-Complex Backpropagation Algorithm for Complex-Valued Neural Networks |
| title_sort | convergence of batch split complex backpropagation algorithm for complex valued neural networks |
| url | http://dx.doi.org/10.1155/2009/329173 |
| work_keys_str_mv | AT huishengzhang convergenceofbatchsplitcomplexbackpropagationalgorithmforcomplexvaluedneuralnetworks AT chaozhang convergenceofbatchsplitcomplexbackpropagationalgorithmforcomplexvaluedneuralnetworks AT weiwu convergenceofbatchsplitcomplexbackpropagationalgorithmforcomplexvaluedneuralnetworks |